In the play 'The Merchant of Venice' by William Shakespeare, Jessica, the daughter of Shylock (a ruthless jewish moneylender) seems to be ashamed of her father and his despicable money-grabbing ways - she is socially embarrassed by him and would like to break the connection but can see only one way to escape and that is marriage. If she married a Christian then she would in a way be 'laundering' her social status awful as that sounds to us today. As she says herself :

"I shall be saved by my husband. He hath made me a Christian"

The lines

'what heinous sin is it in me

To be ashamed to be my father’s child!

But though I am a daughter to his blood,

I am not to his manners. O Lorenzo,

If thou keep promise, I shall end this strife,

Become a Christian and thy loving wife.'

she means that just because she is Shylock's daughter doesn't mean she is like him. She makes a vow that if Lorenzo keeps a promise to her, she will marry him and become a Christian. The word 'heinous' is worse than just 'bad' or 'wrong' as it usually involves some form of unforgivable criminal wrongdoing so she is being very hard on herself herre and her language couldn't be any stronger so Shakespeare shows us how strongly she feels on this matter.